Conservative algebras of 2-dimensional algebras, II

ABSTRACT

In 1990 Kantor defined the conservative algebra W(n) of all algebras (i.e. bilinear maps) on the n-dimensional vector space. If n>1, then the algebra W(n) does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents of W(2). Also similar problems are solved for the algebra W₂ of all commutative algebras on the 2-dimensional vector space and for the algebra S₂ of all commutative algebras with trace zero multiplication on the 2-dimensional vector space.

KEYWORDS:

• Automorphism
• bilinear maps
• conservative algebra
• ideal
• idempotent

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 15A03
• 15A69
• 17A30
• 17A36